One technique for guiding an elevator in a shaft is to mount a sliding shoe assembly to the elevator car and to mount a corresponding guiderail in the hoistway. One prior art shoe assembly uses a plastic U-shaped gib in sliding contact with the rail. Backlash of such gibs typically ranges from 0.6 mm, when new, up to 4.0 mm, when worn. Backlash is inversely proportional to riding comfort. Another prior art shoe uses three plastic gibs, arranged in a U-shape, and pegged on their outside (the side away from the rail) to a mounting bracket. The backlash problems are the same as for the unitary U-shaped gib, plus replacement of the gibs requires complete disassembly from an associated bracket due to the peg-retention feature.